Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 24, 144, 24
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,12}*576a
   3-fold quotients : {2,12,4}*384b
   4-fold quotients : {2,12,6}*288a, {2,6,12}*288d
   6-fold quotients : {2,12,4}*192b, {2,12,4}*192c, {2,6,4}*192
   8-fold quotients : {2,6,6}*144a
   12-fold quotients : {2,12,2}*96, {2,4,6}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   24-fold quotients : {2,3,4}*48, {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,4,2}*32
   48-fold quotients : {2,2,3}*24, {2,3,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  8,  9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)
( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 40, 41)
( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)( 56, 69)
( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 75,111)( 76,113)
( 77,112)( 78,114)( 79,115)( 80,117)( 81,116)( 82,118)( 83,119)( 84,121)
( 85,120)( 86,122)( 87,135)( 88,137)( 89,136)( 90,138)( 91,139)( 92,141)
( 93,140)( 94,142)( 95,143)( 96,145)( 97,144)( 98,146)( 99,123)(100,125)
(101,124)(102,126)(103,127)(104,129)(105,128)(106,130)(107,131)(108,133)
(109,132)(110,134);;
s2 := (  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 95)(  8, 96)(  9, 98)( 10, 97)
( 11, 91)( 12, 92)( 13, 94)( 14, 93)( 15, 75)( 16, 76)( 17, 78)( 18, 77)
( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 79)( 24, 80)( 25, 82)( 26, 81)
( 27, 99)( 28,100)( 29,102)( 30,101)( 31,107)( 32,108)( 33,110)( 34,109)
( 35,103)( 36,104)( 37,106)( 38,105)( 39,123)( 40,124)( 41,126)( 42,125)
( 43,131)( 44,132)( 45,134)( 46,133)( 47,127)( 48,128)( 49,130)( 50,129)
( 51,111)( 52,112)( 53,114)( 54,113)( 55,119)( 56,120)( 57,122)( 58,121)
( 59,115)( 60,116)( 61,118)( 62,117)( 63,135)( 64,136)( 65,138)( 66,137)
( 67,143)( 68,144)( 69,146)( 70,145)( 71,139)( 72,140)( 73,142)( 74,141);;
s3 := (  3, 10)(  4,  9)(  5,  8)(  6,  7)( 11, 14)( 12, 13)( 15, 22)( 16, 21)
( 17, 20)( 18, 19)( 23, 26)( 24, 25)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 35, 38)( 36, 37)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 47, 50)( 48, 49)
( 51, 58)( 52, 57)( 53, 56)( 54, 55)( 59, 62)( 60, 61)( 63, 70)( 64, 69)
( 65, 68)( 66, 67)( 71, 74)( 72, 73)( 75, 82)( 76, 81)( 77, 80)( 78, 79)
( 83, 86)( 84, 85)( 87, 94)( 88, 93)( 89, 92)( 90, 91)( 95, 98)( 96, 97)
( 99,106)(100,105)(101,104)(102,103)(107,110)(108,109)(111,118)(112,117)
(113,116)(114,115)(119,122)(120,121)(123,130)(124,129)(125,128)(126,127)
(131,134)(132,133)(135,142)(136,141)(137,140)(138,139)(143,146)(144,145);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  8,  9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)
( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)
( 40, 41)( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)
( 56, 69)( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 75,111)
( 76,113)( 77,112)( 78,114)( 79,115)( 80,117)( 81,116)( 82,118)( 83,119)
( 84,121)( 85,120)( 86,122)( 87,135)( 88,137)( 89,136)( 90,138)( 91,139)
( 92,141)( 93,140)( 94,142)( 95,143)( 96,145)( 97,144)( 98,146)( 99,123)
(100,125)(101,124)(102,126)(103,127)(104,129)(105,128)(106,130)(107,131)
(108,133)(109,132)(110,134);
s2 := Sym(146)!(  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 95)(  8, 96)(  9, 98)
( 10, 97)( 11, 91)( 12, 92)( 13, 94)( 14, 93)( 15, 75)( 16, 76)( 17, 78)
( 18, 77)( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 79)( 24, 80)( 25, 82)
( 26, 81)( 27, 99)( 28,100)( 29,102)( 30,101)( 31,107)( 32,108)( 33,110)
( 34,109)( 35,103)( 36,104)( 37,106)( 38,105)( 39,123)( 40,124)( 41,126)
( 42,125)( 43,131)( 44,132)( 45,134)( 46,133)( 47,127)( 48,128)( 49,130)
( 50,129)( 51,111)( 52,112)( 53,114)( 54,113)( 55,119)( 56,120)( 57,122)
( 58,121)( 59,115)( 60,116)( 61,118)( 62,117)( 63,135)( 64,136)( 65,138)
( 66,137)( 67,143)( 68,144)( 69,146)( 70,145)( 71,139)( 72,140)( 73,142)
( 74,141);
s3 := Sym(146)!(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 11, 14)( 12, 13)( 15, 22)
( 16, 21)( 17, 20)( 18, 19)( 23, 26)( 24, 25)( 27, 34)( 28, 33)( 29, 32)
( 30, 31)( 35, 38)( 36, 37)( 39, 46)( 40, 45)( 41, 44)( 42, 43)( 47, 50)
( 48, 49)( 51, 58)( 52, 57)( 53, 56)( 54, 55)( 59, 62)( 60, 61)( 63, 70)
( 64, 69)( 65, 68)( 66, 67)( 71, 74)( 72, 73)( 75, 82)( 76, 81)( 77, 80)
( 78, 79)( 83, 86)( 84, 85)( 87, 94)( 88, 93)( 89, 92)( 90, 91)( 95, 98)
( 96, 97)( 99,106)(100,105)(101,104)(102,103)(107,110)(108,109)(111,118)
(112,117)(113,116)(114,115)(119,122)(120,121)(123,130)(124,129)(125,128)
(126,127)(131,134)(132,133)(135,142)(136,141)(137,140)(138,139)(143,146)
(144,145);
poly := sub<Sym(146)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope